{"paper":{"title":"Analytic umbral transmutations and Bessel moments","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Giuseppe Dattoli, Roberto Ricci","submitted_at":"2026-05-27T21:44:19Z","abstract_excerpt":"We develop an analytic umbral approach to Bessel moments, using them as a concrete testbed justifying the passage from formal indicial umbral calculus to Mellin--Barnes umbral transmutation theory. [...] While the formal procedure reproduces the correct results in suitable convergence chambers, it may lead to non-admissible hypergeometric expansions at physically relevant parameter values. The cubic moment provides the basic example [...]\n  We show that this obstruction is removed by replacing the purely formal expansion with an analytic umbral transmutation. In this setting, exponential umbra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05214","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05214/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}